[EM] Steph--median & your criterion

MIKE OSSIPOFF nkklrp at hotmail.com
Fri Jan 17 23:51:44 PST 2003

Mike --

I will try to be more specific and link my criteria to a more fundamental

Voter median is a very insteresting concept. I suppose you consider this
the candidate that could recover the highest number of vote by removing
all candidates to its right or its left if you could align all candidates 
a unidimensional ranked line.

I reply:

A voter-median candidate has as equally many voters to each side
of him in a 1-dimensional issue space or policical spectrum. That's
how it's defined.

You continued:

Some would argue it is a circle and the
extremities depend on every voter lower preferences... In fact this previous
has several holes because it is very hard to formalize. Do you
have a formal definition? Be my guest...
If you ask for thoroughness you have to be prepared to fulfil it too.

I reply:

Above in this reply I defined a voter-median candidate. If that
definition isn't acceptable to you, then you should feel free to
tell me which part of it you don't understand.

You continued:

Or we can simply admit it is the equivalent of the approval winner if
we do not bother being method dependent. It is what you seem
to say below. Am I right?

No, you're wrong. And I couldn't find the place in your quotation
where I'd defined the median in terms of the Approval voting system.

You continued:


>Steph wrote:
>I do not hate Middle, I just dislike under and over representation
>when it comes from the system...
>In a sense every voting system's result comes from "the system".
>But when, with Approval, the voters keep to the voter median,
>that also comes from expressed wishes of a majority of the voters.

Let's suppose we can come up with a median voter definition.

I reply:

That's a safe supposition, because we've had one for quite a long
time here, and in voting system literature. It's the one that I
quoted earlier in this message.

You continued:

Would you agree that adding candidates to some extremity should not
alter the result? Or the method would be cloning or crowding dependent?

I reply:

We all agree that clone independence is desirable, but I don't know
what you mean by crowding independence. As for adding candidates to
an extreme, I don't like they way in which that can change the outcome
in IRV, but, for me, it isn't a standard that I'd write a criterion

I'd said:

>Maybe, but defining your criteria isn't nearly enough. Did you notice
>that I kept asking you if you could justify your criterion in terms
>of something more fundamental? Is it that you didn't notice that,
>or is it that you can't justify the criterion?

You replied:

Using methods that verify my criteria, adding a new candidate should only 
the two
neighbour subsets because this new candidate would represent better the idea 
voters in the available ranges of ranking. Using other methos like approval 
Because the new comer could have the exact balanced position that maximises
the acceptance of its two neighbour groups (and even groups further with
On the other side of the rainbow, other voters will change their mind 
this new possibility. It highers the possibility of the first side finding 
optimal agreement,
so the second side HAS to play it safer and will conceide by accepting a 
"median" or centrist
candidate.Use Alex or Bart strategy with utilities, the maths confirm.

I reply:

I don't recognize that as a fundamental standard. But if someone
else on EM does, then, for them, as for you, you've succeeded in
justifying your criterion in terms of a fundamental standard.

But in Approval, voters have incentive to vote for the voter-median
candidate in order to avoid the election of someone whom they
like less or dislike more.

You continued:

The result is: methods that do not respect the "reciprocal fairness" 
are extremist-candidate-dependent.

I reply:

You've got to demonstrate that more carefully & clearly.

And you should put it in terms of a standard that we already accept.

MOre tomorrow,
Mike Ossipoff

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